Abstract
In this paper, a portfolio-level Liquidity Adjusted Value at Risk model is formulated by using the adapted approach based on the Cornish-Fisher expansion technique to account for non-normality in liquidity risk. Most models ignore the fact that liquidity costs which measure market liquidity are non-normally distributed and this leads to a severe underestimation of the total risk. The Cornish-Fisher expansion technique, as proposed by prior studies is used for correcting the percentiles of a standard normal distribution for non-normality and is simple to implement in practice. The empirical evidence obtained in this study shows that accounting for non-normality at portfolio level and using the modified approach produces much more accurate results than alternative risk estimation methodologies. The model is tested using emerging markets’ data as research on liquidity that primarily focuses on emerging markets yield particularly powerful tests and useful independent evidence since liquidity premium is an important feature of these data.
Highlights
Large and random security price movements during financial crises cause liquidity gaps and most hedging strategies tend to fail when these crises occur
The data on Indian stocks is used for the empirical part of the analysis as research on liquidity that primarily focuses on emerging markets yield powerful tests and useful independent evidence since the liquidity premium is an important feature of these data (Bekaert et al 2007)
This study discusses the approach for calculating a portfolio-level liquidity-adjusted VaR (LVaR) (Modified) measure by using the adapted model based on the Cornish-Fisher expansion technique used for correcting the percentiles of a standard normal distribution for non-normality
Summary
Large and random security price movements during financial crises cause liquidity gaps and most hedging strategies tend to fail when these crises occur. There are many alternative measures of liquidity in the literature such as quoted bid-ask spreads, effective bid-ask spreads, turnover, the ratio of absolute returns-to-volume, adverse-selection and market-making cost components of price impact (Korajczyk and Sadka 2008). Prior studies have analyzed the importance of liquidity risk using a comprehensive liquidity measure in a Value-at-Risk (VaR) framework (Jarrow and Subramaniam 1997, Bangia et al 2002, Angelidis and Benos 2006, Stange and Kaserer 2011). Most LVaR models ignore the fact that liquidity costs, which measure market liquidity, are non-normally distributed displaying fat tails and skewness. Stange and Kaserer (2008) analyze the distributional properties of liquidity costs and show that they are heavily skewed and fat-tailed. The argument of non-normality holds for liquidity costs. Stange and Kaserer (2008) analyze the distributional properties of liquidity costs and show that they are heavily skewed and fat-tailed. Ernst et al (2012) suggest a parametric approach based on the Cornish–Fisher approximation to account for non-normality in liquidity risk
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